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We present the discovery of the giant planet KELT-19Ab, which transits the moderately bright $(\mathrm{V} \sim 9.9)$ A8V star TYC 764-1494-1 with an orbital period of 4.61 days. We confirm the planetary nature of the companion via a combination of radial velocities, which limit the mass to $< 4.1\,\mathrm{M_J}$ $(3\sigma)$, and a clear Doppler tomography signal, which indicates a retrograde projected spin-orbit misalignment of $\lambda = -179.7^{+3.7}_{-3.8}$ degrees. Global modeling indicates that the $\rm{T_{eff}} =7500 \pm 110\,\mathrm{K}$ host star has $\mathrm{M_*} = 1.62^{+0.25}_{-0.20}\,\mathrm{M_\odot}$ and $\mathrm{R_*} = 1.83 \pm 0.10\,\mathrm{R_\odot}$. The planet has a radius of $\mathrm{R_P}=1.91 \pm 0.11\,\mathrm{R_J}$ and receives a stellar insolation flux of $\sim 3.2\times 10^{9}\,\mathrm{erg\,s^{-1}\,cm^{-2}}$, leading to an inferred equilibrium temperature of $\rm{T_{EQ}} = \sim 1935\,\rm{K}$ assuming zero albedo and complete heat redistribution. With a $v\sin{I_*}=84.8\pm 2.0\,\mathrm{km\,s^{-1}}$, the host is relatively slowly rotating compared to other stars with similar effective temperatures, and it appears to be enhanced in metallic elements but deficient in calcium, suggesting that it is likely an Am star. KELT-19A would be the first detection of an Am host of a transiting planet of which we are aware. Adaptive optics observations of the system reveal the existence of a companion with late G9V/early K1V spectral type at a projected separation of $\approx 160\,\mathrm{AU}$. Radial velocity measurements indicate that this companion is bound. Most Am stars are known to have stellar companions, which are often invoked to explain the relatively slow rotation of the primary. In this case, the stellar companion is unlikely to have caused the tidal braking of the primary. However, it may have emplaced the transiting planetary companion via the Kozai-Lidov mechanism., Comment: Published in The Astronomical Journal. 18 pages, 14 figures, 6 tables